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A144304 Square array A(n,m), n>=0, m>=0, read by antidiagonals: A(n,m) = n-th number of the m-th iteration of the hyperbinomial transform on sequence A001858. 2
1, 1, 1, 1, 2, 2, 1, 3, 7, 7, 1, 4, 14, 38, 38, 1, 5, 23, 93, 291, 291, 1, 6, 34, 178, 822, 2932, 2932, 1, 7, 47, 299, 1763, 9193, 36961, 36961, 1, 8, 62, 462, 3270, 21504, 125292, 561948, 561948, 1, 9, 79, 673, 5523, 43135, 313585, 2022555, 10026505, 10026505, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Antidiagonals n = 0..140, flattened

N. J. A. Sloane, Transforms

EXAMPLE

Square array begins:

   1,   1,   1,    1,    1, ...

   1,   2,   3,    4,    5, ...

   2,   7,  14,   23,   34, ...

   7,  38,  93,  178,  299, ...

  38, 291, 822, 1763, 3270, ...

MAPLE

hymtr:= proc(p) proc(n, m) `if`(m=0, p(n), m*add(p(k) *binomial(n, k) *(n-k+m)^(n-k-1), k=0..n)) end end: f:= proc(n) option remember; add(add(binomial(m, j) *binomial(n-1, n-m-j) *n^(n-m-j) *(m+j)!/ (-2)^j/ m!, j=0..m), m=0..n) end: A:= hymtr(f): seq(seq(A(n, d-n), n=0..d), d=0..12);

MATHEMATICA

hymtr[p_] := Function[{n, m}, If[m == 0, p[n], m*Sum[p[k]*Binomial[n, k]*(n-k+m)^(n-k-1), {k, 0, n}]]]; f[0] = 1; f[n_] := f[n] = Sum[Sum[Binomial[m, j]*Binomial[n-1, n-m-j]*n^(n-m-j)*(m+j)!/(-2)^j/m!, {j, 0, m}], {m, 0, n}]; A[0, _] = 1; A[1, k_] := k+1; A[n_, m_] := hymtr[f][n, m]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-Fran├žois Alcover, Dec 27 2013, translated from Maple *)

CROSSREFS

Columns m=0-3 give: A001858, A001858(n+1), A089462, A089465.

Rows n=0-2 give: A000012, A000027, A008865(m+2).

Main diagonal gives A252727.

Sequence in context: A007441 A289192 A111933 * A122941 A297622 A059584

Adjacent sequences:  A144301 A144302 A144303 * A144305 A144306 A144307

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 17 2008

STATUS

approved

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Last modified January 21 00:46 EST 2022. Contains 350473 sequences. (Running on oeis4.)